Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  int num;
  cin >> num;
  for (int i = 1; i <= 2 * sqrt(num); i++) {
    int x = (i * (i + 1)) / 2;
    int tmp = num - x;
    int st = 1, en = 2 * sqrt(num);
    while (st <= en) {
      int mid = st + (en - st) / 2;
      int y = (mid * (mid + 1)) / 2;
      if (y == tmp) {
        cout << "YES" << endl;
        return 0;
      } else if (y < tmp) {
        st = mid + 1;
      } else {
        en = mid - 1;
      }
    }
  }
  cout << "NO" << endl;
}